Conventional processes for producing olefin polymers generally employ a catalyst system consisting of a solid titanium compound (composed mainly of titanium trichloride) and an organoaluminum compound, or a catalyst system comprising a solid which is titanium tetrachloride supported on magnesium chloride, an organoaluminum compound and an electron-donating compound. Also, there is proposed a process using a polymerization catalyst consisting of a cyclopentadienyl compound of titanium, zirconium or hafnium and an aluminoxane [e.g. Japanese Patent Application Kokai (Laid-Open) No. 19309/1983 (U.S. Pat. No. 4,542,199), Japanese Patent Application Kokai (Laid-Open) No. 217209/1985]. These processes using said polymerization catalysts are defective in that the olefin polymers, particularly, the propylene polymer obtained has a small molecular weight.
Meanwhile, a process for producing olefin polymers is proposed which uses, as part of the catalyst components, Ti(OR).sub.n X.sub.4-n and an aromatic hydrocarbon compound having at least 1 hydroxyl group (U.S. Pat. No. 4,525,556). The catalyst system used in this process, however, further requires, as other essential catalyst components, MgR.sub.2 and an inorganic or organic halogen compound and furthermore requires, as an organoaluminum compound, AlR.sub.n X.sub.n' (wherein R is a hydrocarbon group, X is halogen, n and n' are each a value of 0 to 3 and n+n'=3).